{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "Chapter 13\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Code from previous chapters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`make_system`, `plot_results`, and `calc_total_infected` are unchanged."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_system(beta, gamma):\n",
    "    \"\"\"Make a system object for the SIR model.\n",
    "    \n",
    "    beta: contact rate in days\n",
    "    gamma: recovery rate in days\n",
    "    \n",
    "    returns: System object\n",
    "    \"\"\"\n",
    "    init = State(S=89, I=1, R=0)\n",
    "    init /= np.sum(init)\n",
    "\n",
    "    t0 = 0\n",
    "    t_end = 7 * 14\n",
    "\n",
    "    return System(init=init, t0=t0, t_end=t_end,\n",
    "                  beta=beta, gamma=gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_results(S, I, R):\n",
    "    \"\"\"Plot the results of a SIR model.\n",
    "    \n",
    "    S: TimeSeries\n",
    "    I: TimeSeries\n",
    "    R: TimeSeries\n",
    "    \"\"\"\n",
    "    plot(S, '--', label='Susceptible')\n",
    "    plot(I, '-', label='Infected')\n",
    "    plot(R, ':', label='Recovered')\n",
    "    decorate(xlabel='Time (days)',\n",
    "             ylabel='Fraction of population')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_total_infected(results):\n",
    "    \"\"\"Fraction of population infected during the simulation.\n",
    "    \n",
    "    results: DataFrame with columns S, I, R\n",
    "    \n",
    "    returns: fraction of population\n",
    "    \"\"\"\n",
    "    return get_first_value(results.S) - get_last_value(results.S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_simulation(system, update_func):\n",
    "    \"\"\"Runs a simulation of the system.\n",
    "        \n",
    "    system: System object\n",
    "    update_func: function that updates state\n",
    "    \n",
    "    returns: TimeFrame\n",
    "    \"\"\"\n",
    "    init, t0, t_end = system.init, system.t0, system.t_end\n",
    "    \n",
    "    frame = TimeFrame(columns=init.index)\n",
    "    frame.row[t0] = init\n",
    "    \n",
    "    for t in linrange(t0, t_end):\n",
    "        frame.row[t+1] = update_func(frame.row[t], t, system)\n",
    "    \n",
    "    return frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_func(state, t, system):\n",
    "    \"\"\"Update the SIR model.\n",
    "    \n",
    "    state: State (s, i, r)\n",
    "    t: time\n",
    "    system: System object\n",
    "    \n",
    "    returns: State (sir)\n",
    "    \"\"\"\n",
    "    beta, gamma = system.beta, system.gamma\n",
    "    s, i, r = state\n",
    "\n",
    "    infected = beta * i * s    \n",
    "    recovered = gamma * i\n",
    "    \n",
    "    s -= infected\n",
    "    i += infected - recovered\n",
    "    r += recovered\n",
    "    \n",
    "    return State(S=s, I=i, R=r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sweeping beta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a range of values for `beta`, with constant `gamma`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_array = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 , 1.1]\n",
    "gamma = 0.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the simulation once for each value of `beta` and print total infections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1 0.010756340768063644\n",
      "0.2 0.11898421353185373\n",
      "0.3 0.5890954199973404\n",
      "0.4 0.8013385277185551\n",
      "0.5 0.8965769637207062\n",
      "0.6 0.942929291399791\n",
      "0.7 0.966299311298026\n",
      "0.8 0.9781518959989762\n",
      "0.9 0.9840568957948106\n",
      "1.0 0.9868823507202488\n",
      "1.1 0.988148177093735\n"
     ]
    }
   ],
   "source": [
    "for beta in beta_array:\n",
    "    system = make_system(beta, gamma)\n",
    "    results = run_simulation(system, update_func)\n",
    "    print(system.beta, calc_total_infected(results))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wrap that loop in a function and return a `SweepSeries` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sweep_beta(beta_array, gamma):\n",
    "    \"\"\"Sweep a range of values for beta.\n",
    "    \n",
    "    beta_array: array of beta values\n",
    "    gamma: recovery rate\n",
    "    \n",
    "    returns: SweepSeries that maps from beta to total infected\n",
    "    \"\"\"\n",
    "    sweep = SweepSeries()\n",
    "    for beta in beta_array:\n",
    "        system = make_system(beta, gamma)\n",
    "        results = run_simulation(system, update_func)\n",
    "        sweep[system.beta] = calc_total_infected(results)\n",
    "    return sweep"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sweep `beta` and plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.1</th>\n",
       "      <td>0.010756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.2</th>\n",
       "      <td>0.118984</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.3</th>\n",
       "      <td>0.589095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.4</th>\n",
       "      <td>0.801339</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.5</th>\n",
       "      <td>0.896577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.6</th>\n",
       "      <td>0.942929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.7</th>\n",
       "      <td>0.966299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.8</th>\n",
       "      <td>0.978152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.9</th>\n",
       "      <td>0.984057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>0.986882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.1</th>\n",
       "      <td>0.988148</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "0.1    0.010756\n",
       "0.2    0.118984\n",
       "0.3    0.589095\n",
       "0.4    0.801339\n",
       "0.5    0.896577\n",
       "0.6    0.942929\n",
       "0.7    0.966299\n",
       "0.8    0.978152\n",
       "0.9    0.984057\n",
       "1.0    0.986882\n",
       "1.1    0.988148\n",
       "dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "infected_sweep = sweep_beta(beta_array, gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure to file figs/chap13-fig01.pdf\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "label = 'gamma = ' + str(gamma)\n",
    "plot(infected_sweep, label=label)\n",
    "\n",
    "decorate(xlabel='Contact rate (beta)',\n",
    "         ylabel='Fraction infected')\n",
    "\n",
    "savefig('figs/chap13-fig01.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sweeping gamma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the same array of values for `beta`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta_array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now an array of values for `gamma`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.2, 0.4, 0.6, 0.8]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gamma_array = [0.2, 0.4, 0.6, 0.8]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each value of `gamma`, sweep `beta` and plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure to file figs/chap13-fig02.pdf\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 4))\n",
    "\n",
    "for gamma in gamma_array:\n",
    "    infected_sweep = sweep_beta(beta_array, gamma)\n",
    "    label = 'gamma = ' + str(gamma)\n",
    "    plot(infected_sweep, label=label)\n",
    "    \n",
    "decorate(xlabel='Contact rate (beta)',\n",
    "         ylabel='Fraction infected',\n",
    "         loc='upper left')\n",
    "\n",
    "plt.legend(bbox_to_anchor=(1.02, 1.02))\n",
    "plt.tight_layout()\n",
    "savefig('figs/chap13-fig02.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:**  Suppose the infectious period for the Freshman Plague is known to be 2 days on average, and suppose during one particularly bad year, 40% of the class is infected at some point.  Estimate the time between contacts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.1</th>\n",
       "      <td>0.002736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.2</th>\n",
       "      <td>0.007235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.3</th>\n",
       "      <td>0.015929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.4</th>\n",
       "      <td>0.038603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.5</th>\n",
       "      <td>0.132438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.6</th>\n",
       "      <td>0.346765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.7</th>\n",
       "      <td>0.530585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.8</th>\n",
       "      <td>0.661553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.9</th>\n",
       "      <td>0.754595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>0.821534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.1</th>\n",
       "      <td>0.870219</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "0.1    0.002736\n",
       "0.2    0.007235\n",
       "0.3    0.015929\n",
       "0.4    0.038603\n",
       "0.5    0.132438\n",
       "0.6    0.346765\n",
       "0.7    0.530585\n",
       "0.8    0.661553\n",
       "0.9    0.754595\n",
       "1.0    0.821534\n",
       "1.1    0.870219\n",
       "dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Sweep beta with fixed gamma\n",
    "gamma = 1/2\n",
    "infected_sweep = sweep_beta(beta_array, gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.62548698])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Interpolating by eye, we can see that the infection rate passes through 0.4\n",
    "# when beta is between 0.6 and 0.7\n",
    "# We can use the `crossings` function to interpolate more precisely\n",
    "# (although we don't know about it yet :)\n",
    "beta_estimate = crossings(infected_sweep, 0.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.59875429])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Time between contacts is 1/beta\n",
    "time_between_contacts = 1/beta_estimate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SweepFrame\n",
    "\n",
    "The following sweeps two parameters and stores the results in a `SweepFrame`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sweep_parameters(beta_array, gamma_array):\n",
    "    \"\"\"Sweep a range of values for beta and gamma.\n",
    "    \n",
    "    beta_array: array of infection rates\n",
    "    gamma_array: array of recovery rates\n",
    "    \n",
    "    returns: SweepFrame with one row for each beta\n",
    "             and one column for each gamma\n",
    "    \"\"\"\n",
    "    frame = SweepFrame(columns=gamma_array)\n",
    "    for gamma in gamma_array:\n",
    "        frame[gamma] = sweep_beta(beta_array, gamma)\n",
    "    return frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the `SweepFrame` look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0.2</th>\n",
       "      <th>0.4</th>\n",
       "      <th>0.6</th>\n",
       "      <th>0.8</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.1</th>\n",
       "      <td>0.010756</td>\n",
       "      <td>0.003642</td>\n",
       "      <td>0.002191</td>\n",
       "      <td>0.001567</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.2</th>\n",
       "      <td>0.118984</td>\n",
       "      <td>0.010763</td>\n",
       "      <td>0.005447</td>\n",
       "      <td>0.003644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.3</th>\n",
       "      <td>0.589095</td>\n",
       "      <td>0.030185</td>\n",
       "      <td>0.010771</td>\n",
       "      <td>0.006526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.4</th>\n",
       "      <td>0.801339</td>\n",
       "      <td>0.131563</td>\n",
       "      <td>0.020917</td>\n",
       "      <td>0.010780</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.5</th>\n",
       "      <td>0.896577</td>\n",
       "      <td>0.396409</td>\n",
       "      <td>0.046140</td>\n",
       "      <td>0.017640</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0.2       0.4       0.6       0.8\n",
       "0.1  0.010756  0.003642  0.002191  0.001567\n",
       "0.2  0.118984  0.010763  0.005447  0.003644\n",
       "0.3  0.589095  0.030185  0.010771  0.006526\n",
       "0.4  0.801339  0.131563  0.020917  0.010780\n",
       "0.5  0.896577  0.396409  0.046140  0.017640"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame = sweep_parameters(beta_array, gamma_array)\n",
    "frame.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's how we can plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for gamma in gamma_array:\n",
    "    label = 'gamma = ' + str(gamma)\n",
    "    plot(frame[gamma], label=label)\n",
    "    \n",
    "decorate(xlabel='Contact rate (beta)',\n",
    "         ylabel='Fraction infected',\n",
    "         title='',\n",
    "         loc='upper left')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also plot one line for each value of `beta`, although there are a lot of them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure to file figs/chap13-fig03.pdf\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 4))\n",
    "\n",
    "\n",
    "for beta in [1.1, 0.9, 0.7, 0.5, 0.3]:\n",
    "    label = 'beta = ' + str(beta)\n",
    "    plot(frame.row[beta], label=label)\n",
    "    \n",
    "decorate(xlabel='Recovery rate (gamma)',\n",
    "         ylabel='Fraction infected')\n",
    "\n",
    "plt.legend(bbox_to_anchor=(1.02, 1.02))\n",
    "plt.tight_layout()\n",
    "savefig('figs/chap13-fig03.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's often useful to separate the code that generates results from the code that plots the results, so we can run the simulations once, save the results, and then use them for different analysis, visualization, etc.\n",
    "\n",
    "After running `sweep_parameters`, we have a `SweepFrame` with one row for each value of `beta` and one column for each value of `gamma`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure to file figs/chap13-fig04.pdf\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "contour(frame)\n",
    "\n",
    "decorate(xlabel='Recovery rate (gamma)',\n",
    "         ylabel='Contact rate (beta)',\n",
    "         title='Fraction infected, contour plot')\n",
    "\n",
    "savefig('figs/chap13-fig04.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
